Dispersion relation in oscillatory reaction-diffusion systems with self-consistent flow in true slime mold

In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect...

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Bibliographic Details
Published in:Journal of mathematical biology 2007-06, Vol.54 (6), p.745-760, Article 745
Main Authors: Yamada, H, Nakagaki, T, Baker, R E, Maini, P K
Format: Article
Language:English
Subjects:
Animals
Biological Clocks - physiology
Cytoplasm - physiology
Diffusion
Dispersion
Elongation
Intracellular signalling
Mathematical models
Models, Biological
Nonlinear analysis
Numerical Analysis, Computer-Assisted
Organisms
Oscillators
Physarum
Physarum polycephalum - physiology
Physiological effects
Physiology
Plasmodium
Protoplasm
Protoplasmic streaming
Slime molds
Waves
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Summary:In the large amoeboid organism Physarum, biochemical oscillators are spatially distributed throughout the organism and their collective motion exhibits phase waves, which carry physiological signals. The basic nature of this wave behaviour is not well-understood because, to date, an important effect has been neglected, namely, the shuttle streaming of protoplasm which accompanies the biochemical rhythms. Here we study the effects of self-consistent flow on the wave behaviour of oscillatory reaction-diffusion models proposed for the Physarum plasmodium, by means of numerical simulation for the dispersion relation and weakly nonlinear analysis for derivation of the phase equation. We conclude that the flow term is able to increase the speed of phase waves (similar to elongation of wave length). We compare the theoretical consequences with real waves observed in the organism and also point out the physiological roles of these effects on control mechanisms of intracellular communication.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-006-0067-1